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Simplifying 4x2 + -2x + -84 = 0 Reorder the terms: -84 + -2x + 4x2 = 0 Solving -84 + -2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -42 + -1x + 2x2 = 0 Solving -42 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + -0.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -0.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -0.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -0.5x + x2 = 0 + 21 -0.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -0.5x + x2 = 21 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 21 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 21 + 0.0625 Combine like terms: 21 + 0.0625 = 21.0625 0.0625 + -0.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + -0.25) equal to 4.589389938 and -4.589389938.Subproblem 1
x + -0.25 = 4.589389938 Simplifying x + -0.25 = 4.589389938 Reorder the terms: -0.25 + x = 4.589389938 Solving -0.25 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 4.589389938 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.589389938 + 0.25 x = 4.589389938 + 0.25 Combine like terms: 4.589389938 + 0.25 = 4.839389938 x = 4.839389938 Simplifying x = 4.839389938Subproblem 2
x + -0.25 = -4.589389938 Simplifying x + -0.25 = -4.589389938 Reorder the terms: -0.25 + x = -4.589389938 Solving -0.25 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -4.589389938 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.589389938 + 0.25 x = -4.589389938 + 0.25 Combine like terms: -4.589389938 + 0.25 = -4.339389938 x = -4.339389938 Simplifying x = -4.339389938Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.839389938, -4.339389938}Solution
x = {4.839389938, -4.339389938}
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